Group Axioms for Iteration

Proofs for Group and Abelian Group Single Axioms* Proofs for Group and Abelian Group Single Axioms

This memorandum serves as a companion to the paper \Single axioms for groups and Abelian groups with various operations". That paper presents single axioms for groups and Abelian groups in terms of fproduct, inverseg, fdivisiong, fdouble division, identityg, fdouble division, inverseg, fdivision, identityg, and fdivision, inverseg. Proofs that were omitted from that paper are presented here.

Single Axioms for the Left Group and Right Group Calculi

Basic Process Algebra with Iteration: Completeness of its Equational Axioms

Bergstra, Bethke and Ponse proposed an axiomatization for Basic Process Algebra extended with (binary) iteration. In this paper, we prove that this axiomatization is complete with respect to strong bisimulation equivalence. To obtain this result, we will set up a term rewriting system, based on the axioms, and prove that this term rewriting system is terminating, and that bisimilar normal forms...

Group Recommendations: Axioms, Impossibilities, and Random Walks

We introduce an axiomatic approach to group recommendations, in line of previous work on the axiomatic treatment of trust-based recommendation systems, ranking systems, and other foundational work on the axiomatic approach to internet mechanisms in social choice settings. In group recommendations we wish to recommend to a group of agents, consisting of both opinionated and undecided members, a ...

Aluthge iteration in semisimple Lie group

We extend, in the context of connected noncompact semisimple Lie group, two results of Antezana, Massey, and Stojanoff: Given 0 < λ < 1, (a) the limit points of the sequence {∆λ (X)}m∈N are normal, and (b) lim m→∞‖∆ m λ (X)‖ = r(X), where ‖X‖ is the spectral norm and r(X) is the spectral radius of X ∈ Cn×n and ∆λ(X) is the λ-Aluthge transform of X.